By Seymour Lipschutz
If you'd like most sensible grades and thorough knowing of set thought and similar issues, this strong learn device is the easiest show you could have! It takes you step by step throughout the topic and provides you 530 accompanying similar issues of totally labored strategies. you furthermore may get lots of perform difficulties to do by yourself, operating at your individual velocity. (Answers on the again exhibit you the way you are doing.) This re-creation beneficial properties more advantageous difficulties within the ordinals, cardinals, and transfinite sequence chapters, plus new insurance of actual numbers and integers.
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Additional resources for Schaum's outline of theory and problems of set theory and related topics
Sample text
Examples of the above convolution integral operation are given in Probs. 6. F. 11) CHAPTER 2 Linear Time-Invariant Systems In many applications, the step response s(t) is also a useful characterization of the system. The step response s(t) can be easily determined by Eq. 12) Thus, the step response s(t) can be obtained by integrating the impulse response h(t). Differentiating Eq. 13) Thus, the impulse response h(t) can be determined by differentiating the step response s(t). 3 A. 14) y(t) = Kx(t) where K is a (gain) constant.
Determine whether the system is linear. y, [n] 2 2 -2 - 1 0 1 2 3 4 n -2- 1 0 1 2 3 4 ---+0--+ -2 - 1 0 2 3 4 n n 2 -2- 1 0 1 2 3 4 n Y3[n] x3(nj 3 ---+0--+ 2 -2 - 1 0 1 2 3 4 -2- 1 0 1 2 3 4 n Fig. 1-39 n -- CHAPTER 1 Signals and Systems From Fig. 1-39 it is seen that Thus, if Tis linear, then which is shown in Fig. 1-40. From Figs. 1-39 and 1-40 we see that Hence , the system is not linear. 2 2 2 + -2- 1 0 1 2 3 4 n n - 2- 1 0 1 2 3 4 -2- 1 0 1 2 3 4 n Fig. 42. 67). 116) where x*[n] is the complex conjugate of x[n] .
47. Express the sequences shown in Fig. 1-42 in terms of unit step sequences. x[n] x[n] >- - 4 - 3- 2 - 1 -2- 1 0 1 2 - n N 01 • 4• I I 1 ~ 2 3 - 1 (b) (a) x[n] - 4 - 3- 2 - 1 O 1 2 3 4 5 n (c) Fig. 48. 49. (t), respectively. 50. Let x[n] be an arbitrary sequence with even and odd parts denoted by x,[n] and xJn], respectively. 51. Determine whether or not each of the following signals is periodic. If a signal is periodic , determine its fundamental period. 52. 53. (a) }: (b) }: x[k] = }: x[k] k=O k=no What is lJ(2t)?